Multistage stochastic optimization for private equity investments

Abstract

Long-term investments such as Private Equity (PE), present timing differences in cash inflows and outflows. When allocations in PE are not planned correctly, investors can suffer liquidity problems when paying for unexpected commitments. We present a multistage stochastic optimization model that includes PE assets as free cash flows projects. This model can determine PE allocations, in relation to public equity, under different market settings. Using a factor-based model to construct public and private equity markets, the major findings are: Liquidity problems can be avoided by planning PE allocations in advance and according to market conditions. Our tool reduces commitments taken for more volatile PE market or when investor target is lower. For target returns above 20 per cent, PE allocations enhance portfolio annual returns from 2 to 3 per cent (no volatility increase) only if PE net present value volatility is below 15 per cent. Beyond this point, higher returns comes with more risk. When PE investments are less correlated with public equity, the latter threshold extends to 45 per cent. PE allocation weight changes in time and according to its age. For favorable market conditions and high investors’ appetite, PE investment value can be greater than the entire wealth at some time periods. Leverage option for PE investments decreases performance, even in low PE volatility market. Potential PE gains are offset by debt interest payments and risk becomes higher.